Octagonal symmetry in low‐discrepancy β‐manganese

A low‐discrepancy cubic variant of β‐Mn is presented exhibiting local octagonal symmetry upon projection along any of the three mutually perpendicular 〈100〉 axes. Ideal structural parameters are derived to be and for the P4132 enantiomorph. A comparison of the actual and ideal structure models of β‐...

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Bibliographic Details
Published in:Acta crystallographica. Section A, Foundations and advances Foundations and advances, 2014-09, Vol.70 (5), p.441-447
Main Authors: Hornfeck, Wolfgang, Kuhn, Philipp
Format: Article
Language:English
Subjects:
Crystallography
cubic variant
Foundations
Interatomic distance
low‐discrepancy
Mathematical models
octagonal symmetry
Optimization
Projection
Symmetry
Two dimensional
β‐Mn
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Summary:A low‐discrepancy cubic variant of β‐Mn is presented exhibiting local octagonal symmetry upon projection along any of the three mutually perpendicular 〈100〉 axes. Ideal structural parameters are derived to be and for the P4132 enantiomorph. A comparison of the actual and ideal structure models of β‐Mn is made in terms of the newly devised concept of geometrical discrepancy maps. Two‐dimensional maps of both the geometrical star discrepancy D* and the minimal interatomic distance dmin are calculated over the combined structural parameter range and of generalized β‐Mn type structures, showing that the `octagonal' variant of β‐Mn is almost optimal in terms of globally minimizing D* while at the same time globally maximizing dmin. Geometrical discrepancy maps combine predictive and discriminatory powers to appear useful within a wide range of structural chemistry studies.
ISSN:2053-2733
2053-2733
DOI:10.1107/S2053273314009218